We demonstrate a first-of-its-kind efficient chirped pulse amplification of broadband mid-IR (4-5 μm) femtosecond seed pulse (230 ps, 4μJ) generated in AgGaS2 based OPA driven by Cr:forsterite laser in multi-pass Fe2+:ZnSe amplifier optically pumped by solid-state Q-switched Cr:Yb:Ho:YSGG laser (2.85 μm, 30mJ, 5Hz, 0.6 J/cm2). The system delivers 1.2 mJ at pulse duration of 230 ps. Straightforward compression to 150 fs pulse is achievable with 70% efficiency using diffraction grating pair with peak power of about 6 GW. Further non-linear compression in a bulk CaF2 due to the SPM and anomalous GVD should provide the enhancement of peak power up to 20 GW. Possible routes to reach sub-TW and even TW power level in mid-IR are discussed.